地大23春微积分（一）-模拟题

作业辅导

《微积分(一)》模拟题一.单选题1.求极限(-??
2
?1
)
A.-1
B.0
C.1
D.∞
[答案]:B2.求极限lim
??→01+??
?13
1+??
?1
A.0
B.1
C.1/2
D.3/2
[答案]3.设函数,在,内连续,求??的值.
A.5
B.6
,.7
D.8
[答案]4.求函数y=
x
2
+3??+1,当??=1,?x=0.1时的增量?y.
A.0.1
B.0.2
C.0.3
D.0.4
[答案]5.求极限(
A.1
B.1/2
C.1/3
D.1/4
[答案]:B6.求极限lim
??→∞????????
1??
2A.-1
B.0
C.1
D.2
[答案]:B7.求极限lim
??→0
????????????
??
2??????????
A.1
B.2
C.3
D.4
[答案]:A8.设,.
A.-1
B.0
C.1
,.∞
[答案]:B
[,级属性],
[二级属性]:
[难度]:
[公开度]:9.设,.
A.-1
B.0
C.1
,.2
[答案]
[一级属性]:
,二级属性,:
[难度]:
[公开度]:10.求极限(.
A.-1
B.0
C.1
D.∞
[答案]:C11.求极限

A.-1
B.0
C.1
D.∞
[答案]:B12.求极限

A.1
B.1/2
C.1/3
D.1/4
[答案]:B13.求极限

A.0
B.1
C.2
D.3
[答案]:B14.求极限

A.0
B.1/4
C.1/3
D.3/4
[答案]15.

A.1
B.2
C.3
D.4
[答案]:C16.求极限

A.-1
B.0
C.1
D.∞
[答案]:B17.求极限

A.-1
B.0
C.1
D.∞
[答案]:B18.求极限

A.-1
B.0
C.1
D.∞
[答案]:B19.求极限

A.-1
B.0
C.1
D.∞
[答案]:B20.求极限

A.-1
B.0
C.1
D.∞
[答案]:B21.求极限

A.-1
B.0
C.1
D.∞
[答案]:B22.求极限

A.-1
B.0
C.1
D.∞
[答案]:D23.求极限

A.-1
B.0
C.1
D.∞
[答案]:D24.求极限

A.-1
B.0
C.1
D.∞
[答案]:D25.若
,求a的值
A.1
B.2
C.3
D.4
[答案]:B26.若
,求a,b的值
A.a=1,b=-2
B.a=-1,b=-2
C.a=1,b=2
D.a=-1,b=2
[答案]:A27.求极限

A.-1
B.0
C.1
D.2
[答案]:C28.求极限

A.0
B.1/2
C.1/3
D.1/4
[答案]:C29.求极限

A.0
B.1/2
C.1/3
D.1/4
[答案]:B30.求极限

A.0
B.1
C.2
D.3
[答案]:A31.求极限lim
??→∞
3
??
2
+1
4
??
2
+???1
.A.1/4
B.1/5
C.2/5
D.3/4
[答案]:D32.求极限lim
??→∞（3?
1
??
）（2+
1??
2）
.
A.3
B.4
C.5
D.6
[答案]:D33.求极限lim
??→13
1?
??
3?
1
1???。
.
A.1/2
B.1/3
C.1/4
D.1/5
[答案]:B34.求极限lim
??→1??
2
?3??+1??
2
?2.
A.1
B.2
C.3
D.4
[答案]:D35.求极限lim
??→1??
2
?3??+1??
2
?2.
A.-1
B.0
C.1
D.2
[答案]:C36.求极限lim
??→2（3
x
2
?2x+4）
.
A.11
B.12
C.13
D.14
[答案]:B37.求极限lim
??→0??
??
?
??
?????.
A.-1
B.0
C.1
D.2
[答案]:D38.y=
??
3
?3
??
2
+7的极大值是(),极小值是().
A.5,2
B.7,3
C.6,3
D.5,4
[答案]:B39.设f
x
=
ln1+x，则
f
′′0
=().
A.-1
B.0
C.1
D.2
[答案]:A40.曲线y=
1??在点(1,1)处切线的斜率是().
A.-1/3
B.-1/2
C.1/3
D.1/4
[答案]:B41.设
,则
=()
A.-1
B.0
C.1
D.2
[答案]:B42.若
求a,b的值
A.a=1,b=-1
B.a=1,b=0
C.a=0,b=-1
D.a=-1,b=1
[答案]:A43.

A.1/6
B.1/5
C.1/4
D.1/3
[答案]:A44.已知
求a的值
A.5
B.6
C.7
D.8
[答案]:C45.

A.-1
B.0
C.1
D.2
[答案]:C46.计算

A.-1.25
B.0.5
C.0
D.1.25
[答案]:D47.求

A.-1
B.-1.5
C.0
D.0.5
[答案]:B48.

A.-1
B.0
C.1
D.2
[答案]:B49.设
,则a=(),b=()
A.1
B.2
C.3
D.4
[答案]:C50.函数
的间断点是()
A.-1
B.0
C.1
D.2
[答案]:A51.设
若函数f(x)在其定义域内连续,则k=()
A.1
B.2
C.3
D.4
[答案]:A52.若
,则m=()
A.1
B.2
C.3
D.4
[答案]:D53.
=()
A.-1
B.0
C.1
D.2
[答案]:C54.
=()
A.-1
B.0
C.1
D.2
[答案]:B设f(x)的定义域是[0,1],求
的定义域,由原函数定义域知道后者函数
的范围是[0,1],进而得到x的范围
A.[-1,1]
B.[0,-1]
C.[1,-1]
D.[0,1]
[答案]:A56.
的定义域为
,值域为().
A.[-1,1]
B.[-1,0]
C.[0,1]
D.[-0.5,1]
[答案]:A57.下列函数中,那个不是映射().
A.

B.

C.

D.y=lnx(x>0)
[答案]:B58.曲线
的渐近线条数为()
A.0
B.1
C.2
D.3
[答案]:D59.若,
??
??
+
??
??
=1，求
y
′
等于（）
A.

B.

C.

D.

[答案]:B60.试求lim
??→0
2?
??+4??等于()
A.

B.0
C.1
D.

61.x=-1是函数(的()
A.跳跃间断点
B.可去间断点
C.无穷间断点
D.不是间断点
[答案]:C62.若函数在原函数,下列错误的等式是:
A.

B.

C.

D.

[答案]:B63.仅考虑收益与成本的情况下,获得最大利润的必要条件是:
A.

B.

C.

D.
64.若函数f(x)在
??
0
处不可导,则下列说法正确的是:
A.f(x)在
??
0
处一定不连续
B.f(x)在
??
0
处一定不可微
C.f(x)在
??
0
处的左极限与右极限必有一个不存在
D.f(x)在
??
0
处的左导数与右导数必有一个不存在
[答案]:B65.x=0是函数的()
A.跳跃间断点
B.连续点
C.振荡间断点
D.可去间断点
[答案]:D66.设f(x)为偶函数,φ
??
为奇函数,且??
??(??)
有意义,则??
??(??)
是:
A.偶函数
B.奇函数
C.非奇非偶函数
D.可能奇函数也可能偶函数
[答案]:A67.若
在
处取得最大值,则必有()
A.

B.

C.
且

D.
不存在或

[答案]:B68.下列数列有极限并且极限为1的选项为()
A.

B.

C.

D.

[答案]:D69.x=0是函数
的()
A.连续点
B.可去间断点
C.跳跃间断点
D.无穷间断点
[答案]:B二.判断题1.当
时,
为无穷小
[答案]:T2.无限个无穷小的和不一定是无穷小
[答案]:T3.两个无穷小的商不一定是无穷小;
[答案]:T4.无穷大与无穷大的积也是无穷大
[答案]:T5.无穷小与无穷大的积一定是无穷大
[答案]:F6.无穷小与无穷大的积一定是无穷大
[答案]:F7.

[答案]:T8.两个无穷大的和也是无穷大
[答案]:F9.两个无穷大的和也是无穷小
[答案]:T10.证明:
的充分必要条件是
且

[答案]:T11.

[答案]:T12.

[答案]:T13.

[答案]:T14.

[答案]:T15.

[答案]:T16.

[答案]:T17.证明:对任一数列
,若
且
,则

[答案]:T18.若数列
收敛,而数列
发散,则数列
必发散.
[答案]:T19.若数列
和
都发散,则数列
必发散
[答案]:F20.

[答案]:T21.

[答案]:T三.计算题1.求导数

[答案]:解:
2.求曲线
经过原点的切线方程
[答案]:解:
:切线方程:y=x.3.已知
,求

[答案]:解:
4.设
,其中
在x=a处连续,求
.
[答案]:解
5.已知
,则
=()
[答案]:解:
,
.6.求曲线
在点(1,2)处的切线方程.
[答案]:解:
,切线方程:
.7.求
经过(2,0)的切线方程.
[答案]:设切点为(t,1/t),切线为
,带入(2,0),t=1,切线为
8.求导数

[答案]:解:
9.用洛必达法则求极限

[答案]:解:原式=
10.设
和
是连续函数,试证明
和
也是连续函数.
[答案]:证明:
,
.11.求下列函数的间断点,并指出类型

[答案]:解
,x=0为跳跃间断点12.比较无穷小
与

[答案]:
,当
时
是
的同阶高阶无穷小附件是答案，转载注明 无忧答案网